Choosing the set of parameters given by \(g_{\eta } = 0.088\) , \(m_{\eta } = 20\)  GeV, \(M_{Z^{\prime }}/m_{\eta }\rightarrow 0\) , \(g_{VB} = 8\times 10^{-9}\) , and taking into account the constraint for tan \(2\theta _{\alpha }\) , designated by \(t_{2\alpha }\)  in equation (REF ), we obtain \(s_{\alpha } \simeq -3.8\times 10^{-9}\) . In this case, the spin independent cross section of \(\eta \)  with the nuclei is \(\sigma _{SI}^{p}\approx 2.31\times 10^{-46}\)  cm\(^{2}\)  and \(\sigma _{SI}^{n}\approx 5.42\times 10^{-57}\)  cm\(^{2}\) . The value of \(\sigma _{SI}^{p}\)  is of the same order of magnitude as that of the upper limits obtained by the both the LUX (Large Underground Xenon) experiment and the XENON100 experiment for the WIMP mass range that we consider here [1]}. In our calculations, we obtained our parameters using micromegas package [2]}, [3]}. We note that \(\sigma _{SI}^{n}\)  and \(\sigma _{SI}^{p}\)  are dependent on \(g_{VB}\)  parameter, which in practice connects the dark and visible sectors of the model (cf., Model 2 below)
